Paper summary: A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning

Problem

Sampling many reasoning paths and picking an answer (self-consistency, or choosing by model probability) works in practice, but the theory behind it was thin.

Method

The authors build a theoretical framework that treats these methods as confidence estimation, and analyse two paradigms:

• self-consistency (majority vote): high estimation error
• perplexity (model probability): substantial modelling error, and its estimation error can converge badly

Their method RPC has two parts (Figure 1):

• Perplexity Consistency: combines the two, improving the convergence of estimation error from linear to exponential while keeping model error low
• Reasoning Pruning: removes low-probability reasoning paths to prevent degradation

Key results

From the abstract: across seven benchmarks, RPC matches self-consistency’s reasoning performance while improving confidence reliability and cutting sampling cost by 50%.

Limitations

From the paper: only two typical methods (plus RPC) are analysed in depth, and as a post-hoc selection method its gains are moderate compared with approaches that involve training.